The Belgian striker made amends for an shocking earlier miss four minutes from time to deal last season’s semi-finalists a first defeat of this campaign.
The Blues rode their luck at times, not least when an Ajax goal was ruled out by VAR for the tightest of offside calls, and when the hosts hit the frame of the goal.
But Frank Lampard’s young side grew in stature as a frantic, tetchy encounter wore on and ran out deserved winners when Batshuayi rifled in off the underside of the crossbar.
The memory of a visit from a London club remains raw for Ajax following Tottenham’s dramatic last-four comeback in May, and this was another painful experience for their youthful outfit.
They were fortunate to escape on both counts, while Joel Veltman belted a drive from the edge of the box narrowly wide.
Nerves were fraying on the Chelsea bench as well, with assistant Jody Morris booked for letting his frustration get the better of him.
Ajax had the ball in the net in the 34th minute when Southampton flop turned Ballon D’or nominee Dusan Tadic played in Ziyech, whose attempted curler was deflected into the path of Quincy Promes.
But Chelsea breathed again after VAR ruled that Promes, or at least a microscopic part of him, was offside before he slid the ball home.
Just before half-time Cesar Azpilicueta, a survivor from the last time Chelsea visited the Johan Cruyff Arena in the 2013 Europa League final, was sent clear by Mount but fired high and wide.
The industrious Tammy Abraham was taken off with 20 minutes remaining and replaced by Batshuayi, who immediately missed a glorious chance.
A stray shot ricocheted to the feet of the Belgian, six yards out in front of goal, but he skied his shot horribly.
Another sub, Christian Pulisic, went on a dazzling run before pulling his effort across goal and wide as Chelsea.
But when Pulisic pulled the ball back in the six-yard area Batshuayi was on hand to fire home and a sixth straight win for Lampard’s side.